While separation logic is acknowledged as an enabling technology for large-scale program verification, most of the existing verification tools use only a fragment of separation logic that excludes separating implication. As the first step towards a verification tool using full separation logic, we develop a nested sequent calculus for Boolean BI (Bunched Implications), the underlying theory of separation logic, as well as a theorem prover based on it. A salient feature of our nested sequent calculus is that its sequent may have not only smaller child sequents but also multiple parent sequents, thus producing a graph structure of sequents instead of a tree structure. Our theorem prover is based on backward search in a refinement of the nested sequent calculus in which weakening and contraction are built into all the inference rules. We explain the details of designing our theorem prover and provide empirical evidence of its practicality.
When mechanizing the metatheory of a programming language, one usually needs many lemmas proving structural properties of typing judgments, such as permutation and weakening. Such structural lemmas are sometimes unnecessary if we eliminate typing contexts by expanding typing judgments into their original hypothetical proofs. This technique of eliminating typing contexts, which has been around since Church [4], is based on the view that entailment relations, such as typing judgments, are just syntactic tools for displaying only the hypotheses and conclusion of a hypothetical proof while hiding its internal structure.In this paper, we apply this technique to the POPLmark challenge [1] and experimentally evaluate its efficiency by formalizing System F <: in the Coq proof assistant in a number of different ways. An analysis of our Coq developments shows that eliminating typing contexts produces a more significant reduction in both the number of lemmas and the count of tactics than the cofinite quantification, one of the most effective ways of simplifying the mechanization involving binders. Our experiment with System F <: suggests three guidelines to follow when applying the technique of eliminating typing contexts.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.